Poket Sevens short stack on the bubble

Hey all a recent hand Im wondering about,
Final four in a live tournament forty players. Im the short stack on 85,000 to my left is 150,000 then small is 95,000 and big blind on 250,000. I wake up with poket sevens, I shove and am called by the player to my left with pocket Jacks, I go home crying. The top three get paid in this structure and the prizes are 105 for third, 250 for second and 700 for first I feel like Im at least the second best player and have a good shot if I can get heads up with the big stack. Now normally Im sure shoving is correct, I need to accumulate blinds to stay alive and give myself a shot, however in this situation being on the bubble Im not sure if it it was the correct play, Im finding that I have a tendency to get carried away with pairs in the hole sometimes, not sure if I should be satisfied I made the correct play - though looking to my left could have made me a hundred dollars here perhaps - or if I should adjust my play, being extra tight in that early position out of the blinds on the bubble? Obviously its really a question of how much you adjust on the bubble ensuring you make the cash spots verses giving yourself a good shot at first?
Cheers.

It is hard to analyze the situation without knowing the blinds. However, 77 is a top 10% pushing hand. If you aren't going to play 77, then you are going to be blinding down rapidly. This time, you ran into jacks, but the chance that at least one of the other three players has a higher pair is under 10%.

Casual players often play too loosely early, and then too tightly near the bubble to try to limp into the money. Usually, you want to exploit this pattern, not emulate it. Yes, you are risk-averse, and it would be nice to make the money, but your opponents are risk-averse, too. That means they will call less often, which should encourage you to push with hands of moderate strength. On the bubble, you should call tightly against players who cover you, but usually you should still steal aggressively.

I don't know whether the stack depth would allow you to make a smaller raise. However, medium pairs often have an information disadvantage postflop. Someone with QJ knows whether he hit the flop or not, but you are just going to be guessing most of the time. You should lean toward pushing hands which are hard to play as opposed to making small raises which will get flat-called.

The 700-250-105 structure rewards making the money much less than the 50-30-20 structure for SNGs. One way to look at it is that about 30% of the prize pool (3x105) rewards making the money, as opposed to 60% (3x20%) for a 50-30-20 structure. A flatter structure like 50-30-20 often means you push wider from the SB, but tighter from the CO or earlier. So, you should lean toward pushing more from the CO than you would in a SNG, and even weaker pairs are normally playable from the CO in SNGs. Here are the Nash equilibriums for 700-250-105 and 50-30-20 assuming the blinds are 5,000/10,000. Of course, your opponents may not play according to the Nash equilibrium, but even if they are going to call with every better pair, lots of coin-flips, and few worse pairs, it looks like it is profitable to push 77.